The following line passes through point $(-8, 8)$ : $y = -\dfrac{9}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-8, 8)$ into the equation gives: $8 = -\dfrac{9}{7} \cdot -8 + b$ $8 = \dfrac{72}{7} + b$ $b = 8 - \dfrac{72}{7}$ $b = -\dfrac{16}{7}$ Plugging in $-\dfrac{16}{7}$ for $b$, we get $y = -\dfrac{9}{7} x - \dfrac{16}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-8, 8)$